182 ANNUAL BEPORT SMITHSONIAN INSTITUTION, 193 3 



a force in the Newtonian sense but is a result of the motion that 

 balances the centripetal force of gravitation. 



In order to solve the problem of the motion of any body, we must 

 know in advance certain features of that motion. In the solar sys- 

 tem, for example, we must know whether the motion is nearly circu- 

 lar, like that of the earth around the sun, or highly elliptical, like 

 that of a comet. For this purpose rather rough observations will 

 serve. But when this has become known and an accurate calculation 

 is needed, accurate observations must be used. If observations of the 

 position of a body could be made with perfect accuracy, a very few 

 would suffice. But they are always subject to errors of various 

 kinds, and to diminish the effects of some of these errors the observa- 

 tions must be numerous. Only by continual comparison of the re- 

 sults of theory with the observations can one hope to know the past, 

 and by knowing the past to predict the future. 



The working out of the consequences of the laws of motion and 

 gravitation is almost entirely performed by mathematics. When 

 only two particles are concerned the problem is very simple. With 

 more than two it becomes highly complicated, and a considerable 

 number of the most eminent mathematicians from the time of Newton 

 up to the middle of the nineteenth century attacked it. It is easy to 

 find reasons for the comparative neglect of the problem at the present 

 time : The initiation of other problems in mathematics and astron- 

 omy, the laborious and intricate calculations now necessary if prog- 

 ress is to be made, and the need for assimiliation of a large heritage 

 of the past have all played a part. 



Many astronomical discoveries have been due to the discussion of 

 large numbers of observations. The early tendency of scientific 

 work was to record only the unusual — an eclipse, the appearance of a 

 comet, the time of setting of a bright star or of a planet, and so on. 

 Gravitational astronomy can be said to have made a real start when 

 Tycho Brahe undertook to observe daily over a long period of years 

 sun, moon, planets, and stars, and to record their positions in the 

 sky with all the accuracy his home-made instruments could furnish. 

 Not only so, but he tried to discover all the errors to which his ob- 

 servations were subjected and to correct them accordingly. The next 

 step, that of making deductions from the observations, was taken 

 by Johannes Kepler, who, with some difficulty, managed to get hold 

 of certain of the records left by Tj^cho after the death of the latter. 



Just as Tycho was the forerunner of the tireless routine observer, 

 so Kepler was the first to undertake the discussion of large numbers 

 of observations in order to deduce such laws as he might be able to 

 find. With an immense amount of labor extending over many years 

 he was able to give to the world those that still bear his name. 



